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%I #5 Mar 31 2012 12:37:11
%S 192,96,96,455,181,455,296,232,232,296,1376,534,1340,534,1376,880,686,
%T 682,682,686,880,4111,1589,4007,1581,4007,1589,4111,2622,2042,2030,
%U 2034,2034,2030,2042,2622,12319,4751,12005,4711,12021,4711,12005,4751,12319
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor
%C Table starts
%C ..192...96...455...296..1376...880...4111...2622..12319...7854..36945...23550
%C ...96..181...232...534...686..1589...2042...4751...6110..14239..18318...42705
%C ..455..232..1340...682..4007..2030..12005...6074..35999..18206.107983...54606
%C ..296..534...682..1581..2034..4711...6078..14101..18210..42271..54606..126799
%C .1376..686..4007..2034.12021..6090..36015..18222.107997..54618.323943..163806
%C ..880.1589..2030..4711..6090.14181..18258..42351..54654.126861.163842..380391
%C .4111.2042.12005..6078.36015.18258.108141..54762.324087.163950.971925..491514
%C .2622.4751..6074.14101.18222.42351..54762.127581.164274.381111.491838.1141701
%H R. H. Hardin, <a href="/A206343/b206343.txt">Table of n, a(n) for n = 1..2380</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>10
%F k=2: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>11
%F k=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>12
%F k=4: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>13
%F k=5: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>14
%F k=6: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>15
%F k=7: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) for n>16
%F apparently a(n-1)+3*a(n-2)-3*a(n-3) for n>k+9
%e Some solutions for n=4 k=3
%e ..3..1..3..1....3..2..3..2....0..2..0..1....1..3..0..1....1..1..0..2
%e ..1..3..1..3....2..3..2..3....2..0..2..0....1..0..3..0....3..0..1..0
%e ..3..1..3..1....3..2..3..2....0..2..0..2....0..1..0..3....0..3..0..1
%e ..1..3..1..3....2..3..2..3....1..0..2..0....1..0..1..0....2..0..3..0
%e ..3..1..3..1....3..2..3..2....0..1..0..2....0..1..0..1....0..2..0..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 06 2012
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